I am mainly interested in mathematical models (mainly reaction-diffusion and kinetic) for physical and biological phenomena and their qualitative properties. I have mainly worked on understanding behavior in settings which lack the comparison principle or where traveling waves do not exist -- here traditional methods fail and new results are intimately linked to regularity theory, understanding heat flow, and Hamilton-Jacobi equations. I have also done some work in fluid dynamics and probability.
[arxiv]C^\infty smoothing for weak solutions of the inhomogeneous Landau equation, with Snelson (submitted)
[arxiv]The reactive-telegraph equation and a related kinetic model, with Souganidis (submitted)
[arxiv]Thin front limit of an integro--differential Fisher--KPP equation with fat--tailed kernels, with Bouin, Garnier, Patout (submitted)
[arxiv]Super-linear propagation for a general, local cane toads model, with Perthame, Souganidis (submitted)
[arxiv]Influence of a mortality trade-off on the spreading rate of cane toads fronts, with Bouin, Chan, Kim (submitted)
[arxiv][journ]The Bramson logarithmic delay in the cane toads equation, with Bouin, Ryzhik (Q. Appl. Math. 2017)
[arxiv][journ]Super-linear spreading in local bistable cane toads equations, with Bouin (Nonlinearity 2017)
[arxiv][journ]Ricci curvature bounds for weakly interacting Markov chains, with Erbar, Menz, Tetali (Electron. J. Probab. 2017)
[arxiv][journ]Super-linear spreading in local and non-local cane toads equations, with Bouin, Ryzhik (J. Math. Pures Appl. 2017)
[pdf]Propagation Phenomena in Reaction-Advection-Diffusion Equations (PhD Thesis) (NOTE: All work presented in this thesis is contained in the papers below)
[arxiv][journ]Propagation of solutions to the Fisher-KPP equation with slowly decaying initial data (Nonlinearity 2016)
[arxiv][journ]Equivalence of a mixing condition and the LSI in spin systems with infinite range interaction, with Menz (Stoch. Proc. Appl. 2016)
[arxiv][journ]Stability of Vortex Solutions to an Extended Navier-Stokes System, with Gie, Iyer, Kavlie, Whitehead (Commun. Math. Sci. 2016)
[arxiv][journ]Population Stabilization in Branching Brownian Motion With Absorption, (Commun. Math. Sci. 2016)
[arxiv][journ]Pulsating Fronts in a 2D Reactive Boussinesq System, (Comm. PDEs 2014)